A mass that weighs 8 lb stretches a spring 24 in. The system is acted on by an external force of 4 sin 4t lb. If the mass is pulled down 6 in. and then released, determine the position of the mass at any time. Determine the first four times at which the velocity of the mass is zero

In component form, the displacement vectors become

• 350 m [S]   ==>   (0, -350) m

• 400 m [E 20° N]   ==>   (400 cos(20°), 400 sin(20°)) m

(which I interpret to mean 20° north of east]

• 550 m [N 10° W]   ==>   (550 cos(100°), 550 sin(100°)) m

Then the student's total displacement is the sum of these:

(0 + 400 cos(20°) + 550 cos(100°), -350 + 400 sin(20°) + 550 sin(100°)) m

≈ (280.371, 328.452) m

which leaves the student a distance of about 431.8 m from their starting point in a direction of around arctan(328.452/280.371) ≈ 50° from the horizontal, i.e. approximately 431.8 m [E 50° N].

Answer:

Explanation:

First job is to convert 72 km/hr to m/s:

[tex]72\frac{km}{hr}[/tex] × [tex]\frac{1000m}{1km}[/tex] × [tex]\frac{1hr}{3600s}[/tex] = 2.0 × 10¹ m/s

Now to find the acceleration which is

[tex]a=\frac{v_f-v_0}{t}[/tex] and filling in:

[tex]a=\frac{2.0*10^1-0}{11.5}=1.7\frac{m}{s^2}[/tex] That's part a. Part b want to know how far the car can get in 11.5 seconds (because that's the time it takes for the car to get to 72 km/hr). Since we know that the car can get 2.0 × 10¹ meters in 1 second, that means that in 11.5 seconds, the car can get 11.5(2.0 × 10¹) which is 230 meters.

Answer:

-8.036 kV/m

Explanation:

The electric field E = -ΔV/Δx where ΔV = change in electric potential = V - V' where V = electric potential at x = 5.6 cm =  450 V and V' = electric potential at x = 0 cm, = 0 V . So, ΔV = V - V' = 450 V - 0 V = 450 V.

Δx = distance between the 0 V plate and the 450 V point = 5.6 cm = 0.056 m

So, E = -ΔV/Δx

Substituting the values of the variables into the equation, we have

E = -ΔV/Δx

E = -450 V/0.056 m

E = -8035.7 V/m

E = -8.0357 kV/m

E ≅ -8.036 kV/m

Since the electric field between two parallel conducting plates is constant, the electric field between the plates is E = -8.036 kV/m

Answer:

10 Joule

Explanation:

The solution and answer are well written in the Pic above.

Answer:

519.62 m/s

Explanation:

Applying,

v = √(T/m').............. Equation 1

Where v = velocity of the wave, T = Tension on the string, m' = mass per unit length of the string

From the question,

Given: T = 1350 N, m' = 0.005 kg/m

Substitute these values into equation 1

v = √(1350/0.005)

v = √(270000)

v = 519.62 m/s

Answer:

The fraction of the protons would have no electrons [tex]=1.88\times 10^{-10}[/tex]

Explanation:

We are given that

Amoeba has total number of protons=[tex]1.00\times 10^{16}[/tex]

Net charge, Q=0.300pC

Electrons are fewer than protons=[tex]1.88\times 10^6[/tex]

We have to find the fraction of protons would have no electrons.

The fraction of the protons would have no electrons

=[tex]\frac{Fewer\;electrons}{Total\;protons}[/tex]

The fraction of the protons would have no electrons

=[tex]\frac{1.88\times 10^{6}}{1.00\times 10^{16}}[/tex]

[tex]=1.88\times 10^{-10}[/tex]

Hence, the fraction of the protons would have no electrons [tex]=1.88\times 10^{-10}[/tex]

Explanation:

Mechanical advantage (MA) = Load/Effort. Velocity ratio (VR) = distance effort moves/ distance load moves in the same time

Answer:

1. 100 J

2. 225 J

Explanation:

We'll begin by calculating the mass of the object. This can be obtained as follow:

Velocity (v) = 5 ms¯¹

Kinetic energy (KE) = 25 J

Mass (m) =?

KE = ½mv²

25 = ½ × m × 5²

25 = ½ × m × 25

25 = 25m / 2

Cross multiply

25m = 25 × 2

25m = 50

Divide both side by 25

m = 50 / 25

m = 2 Kg

1. Determination of the kinetic energy when the velocity is doubled.

Mass (m) = 2 Kg

Velocity (v) = double the initial velocity

= 2 × 5 ms¯¹

= 10 ms¯¹

Kinetic energy (KE) =?

KE = ½mv²

KE = ½ × 2 × 10²

KE = ½ × 2 × 100

KE = 100 J

2. Determination of the kinetic energy when the velocity increased three times.

Mass (m) = 2 Kg

Velocity (v) = three times the initial velocity

= 3 × 5 ms¯¹

= 15 ms¯¹

Kinetic energy (KE) =?

KE = ½mv²

KE = ½ × 2 × 15²

KE = ½ × 2 × 225

KE = 225 J

Answer:

A) x4

Explanation:

Magnification is equal to image size divided by the actual size, or M = I/A.

The image size is the student's drawing, which is 28.8 cm, and the actual size is 7.2 cm. Divide them, and cancel out the units, and you should get:

28.8 cm/7.2 cm = 4

Answer 60 NEWTON

Explanation:

FORCE = MASS * acceleration

acceleration= VELOCITY / TIME

acceleration= 30 / 10 = 3   M/S2

FORCE = MASS * acceleration

FORCE = 20 *3 = 60 NEWTON

Answer:

b

Explanation:

bc

Answer:

im pretty sure it should be 50.0

Answer:

(a) t = 0.75 s

(b) d = 26 m

Explanation:

Height, h = 12 m

Angle, A = 30 degree

initial velocity, u = 40 m/s

(a) Let the time is t.

Use second equation of motion

 [tex]h = u t + 0.5 at^2\\\\12 = 40 sin 30 t - 0.5 \times10 \times t^2\\\\12 = 20 t - 5 t^2\\\\5 t^2 - 20 t + 12 =0 \\\\t = \frac{20\pm \sqrt{400-240}}{10}\\\\t = \frac{20\pm 12.65}{10}\\\\t = 3.3 s, 0.75 s[/tex]

(b) d = u cos A t

d = 40 x cos 30 x 0.75 = 26 m

Answer:

Negative ion

.................

Complete question is;

A bicycle and a car start their journey at the same time the cyclist reaches it's top speed of 10m/s in 15 s, the car reaches a speed of 15 m/s in 55 s. which has the greater acceleration the car or the bicycle.

Answer:

The bicycle has the greater acceleration.

Explanation:

Cyclist reaches a top speed of 10m/s in 15 s.

Formula for acceleration here is;

a = v/t

a = 10/15

a = 0.67 m/s²

Car reaches a speed of 15 m/s in 55 s.

Thus;

a = 15/55

a = 0.27 m/s²

From the 2 acceleration values gotten, we can say that;

The bicycle has the greater acceleration.

Answer:

The acceleration of proton is 5.56 x 10^10 m/s^2 .

Explanation:

initial velocity, u = 0

Electric field, E = 580 N/C

final speed, v = 10^6 m/s

(a) Let the acceleration is a.

According to the Newton's second law

F = m a = q E

where, q is the charge of proton and m is the mass.

[tex]a= \frac{q E}{m}\\\\a = \frac{1.6\times10^{-19}\times 580}{1.67\times 10^{-27}}\\\\a= 5.56\times 10^{10} m/s^2[/tex]

Answer:

Mass = 64,870,000,000 kilograms

Explanation:

Given the following data;

Density = 998 kg/m³

Volume = 6,500,000 m³

To find the mass of water in the reservoir;

Density can be defined as mass all over the volume of an object.

Simply stated, density is mass per unit volume of an object.

Mathematically, density is given by the equation;

Density = mass/volume

Making mass the subject of formula, we have;

Mass = density * volume

Mass = 998 * 6,500,000

Mass = 64,870,000,000 kilograms

On a hot dry day, the amount of water vapour present in atmosphere is less. Thus, water present inside the desert cooler evaporates more, thereby cooling the surroundings more. Hence, a desert cooler cools better on a hot dry day.

Answer:

An object overall change in position

Explanation:

ans maybe corre6

Answer:

horizontal velocity remaing constan thorough out the motion but the vertical motion's velocity changes due to the gravity acting on it.

for everl 1 second the velocity decreases by 9.8 that is the gravity

Answer:

4 A

Explanation:

Firstly we need to calculate the equivalent resistance. Since, two resistors of 6 connected in parallel, so equivalent resistance will be given by,

[tex]\longrightarrow[/tex] 1/R = 1/R1 + 1/R2

[tex]\longrightarrow[/tex] 1/R = (1/6 + 1/6) Ω

[tex]\longrightarrow[/tex] 1/R = (1 + 1)/6 Ω

[tex]\longrightarrow[/tex] 1/R = 2/6 Ω

[tex]\longrightarrow[/tex] R = 6/2 Ω

[tex]\longrightarrow[/tex] R = 3 Ω

We know that,

[tex]\longrightarrow[/tex] V = IR

[tex]\longrightarrow[/tex] 12 = I × 3

[tex]\longrightarrow[/tex] 12 ÷ 3 = I

[tex]\longrightarrow[/tex] 4 Ampere = I

If the car's motion appears as a horizontal line on a position-time graph, it shows that as time changes, the car's position doesn't change.

This is just a complicated way to say that the car is not moving. (A)

Answer: It's not moving.

Explanation:

I got it correct on edmentum.

Answer:

Data given.

focal length (f)=15m÷2=7.5m

Distance of the object(U)=10m

Image distance (v)=?

Magnification (M)=?

Solution:

From:

1/f=1/u+1/v

1/7.5=1/10+1/v=75

then v=75m

Magnification, M=u/v

=75/10=7.5

Then magnification=7.5

Answer:

v = 30 m and m = 3

Explanation:

Given that,

The radius of curvature of the mirror, R = 15 m

Focal length, f = 7.5 m

Object distance, u = -10 m

We need to find the image distance and the magnification of the object.

Using mirror's formula,

[tex]\dfrac{1}{v}-\dfrac{1}{u}=\dfrac{1}{f}\\\\\dfrac{1}{v}=\dfrac{1}{f}+\dfrac{1}{u}\\\\\dfrac{1}{v}=\dfrac{1}{(7.5)}+\dfrac{1}{(-10)}\\\\v=30\ m[/tex]

The magnification of the object in mirror is given by :

[tex]m=\dfrac{-v}{u}\\\\m=\dfrac{-30}{-10}\\\\m=3[/tex]

So, the distance of the image from the mirror and the magnification of the object are 30 m and 3 respectively.

The drawing shows the couple acting on a tire wrench is missing and so i have attached it.

We are to find an expression for the torque when the axis is perpendicular to the tire and passes through the points A, B & C

Answer:

Point A: τ = Fl

Point B: τ = 0

Point C: - Fl

Explanation:

Formula for torque is;

τ = F × d

Where;

F is perpendicular force

d is distance.

Thus;

> At point A, it means we are taking torque about point A and so we have;

τ = (-F × 0) + (F × L)

τ = Fl

> At point B, it means we are taking torque about point B and so we have;

τ = (-F × L/2) + (F × L/2)

τ = -(FL/2) + (FL/2)

τ = 0

> At point C, it means we are taking torque about point C and so we have;

τ = (-F × L) + (F × 0)

τ = -FL

Answer:

B

Explanation:

Answer:

150 kJ

Explanation:

Applying,

ΔH = Energy level of Product(E') - Energy level of reactant(E)

Where ΔH = enthalpy change, E' and E = energy level of the product and the reactant respectively

ΔH = E'-E............. Equation 1

From the diagram,

Given: E' = 200 kJ, E = 50 kJ

Substitute these values into equation 1

ΔH = 200-50

ΔH = 150 kJ

Hence the enthalpy change for the reaction is 150 kJ

Answer:

The Mars appears in the direction of South.

Explanation:

Mars is rising in the east at 6: 30 PM. The period of rotation of earth is 24 hours.

So, 6 hours is the one fourth of the period of rotation of earth. Earth rotates counter clockwise on its axis, so after 6 hours, we see the Mars in the direction of South.

"Energy" is the ability to do work.

"Work" is the process of using energy.